`2^1|cosx|+|cosx|^(2 dotx)=4\ \ in\ (-pi,pi)`

If (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))=cot(a+x/2) and x in (pi,2pi) then 'a' is equal to :

Prove that : tan^(-1)((cosx)/(1-sinx))-cot^(-1)(sqrt((1+cosx)/(1-cosx)))=(pi)/(4), x in (0, pi//2) .

Which of the following is/are correct ? (a) (tanx)^(In (cosx))lt(cotx)^(In(cosx))AAx in(pi/4,pi/2 ) (b) (sinx)^(In (secx))gt(cosx)^(In(secx))AA x in(0,pi/4) (c ) (sec. pi/3)^(In (tanx))gt(sec. pi/3)^(In(cosx))AA x in (pi/4,pi/2) (d) (1/2)^(In(sinx))gt(3/4)^(In(sinx))AA x in(0,pi/2)

f(x)= (1-sinx+cosx)/(1+sinx+cosx) discontinuous at x=pi . Find f(pi) so that f(x) is continuous x=pi

Express each of the following in the simplest form: tan^(-1){(cosx)/(1-sinx)},\ -pi/2

int_0^(pi/2) (3+4cosx)/(4+3cosx)^2dx= (A) 3/4 (B) 1/2 (C) pi/4 (D) 1/4